1. Field of the Invention
The present invention applies to the field of training sequences for communications systems and, in particular, to storing a training sequence having desirable correlation properties for peak to average power constrained modulation formats.
2. Description of the Prior Art
Communications systems such as cellular voice and data communication systems typically have several base stations available for use by several mobile or fixed user terminals, such as cellular telephones or wireless web devices. In such systems, base stations and user terminals typically communicate in data bursts. A burst may be a given time slot allocated to a user terminal in which it may communicate with the base station. For synchronization and calibration purposes, each burst includes a training sequence. The training sequence contains a known symbol set transmitted for quality control purposes. Since the data or symbol sequence is known, the characteristics of the received signal can be accurately measured and interpreted. Training sequences can be used for computing spatial and temporal filter weights at a base station in order to reduce intersymbol interference and co-channel interference, and increase the signal to noise ratio.
Two useful characteristics of well-designed training sequences are, first, that the training sequences of different users should be different, and second, that delayed training sequences of the same user should look different from the same training sequences received without delay. The first characteristic is enhanced if the absolute value of the cross correlations of the training sequences of any two users is kept as small as possible. The second characteristic is enhanced if the out of phase autocorrelations of the training sequence of any user are kept as small as possible.
Sequences with these desirable characteristics have been designed in the literature. Some of these sequences include Gold, Kasami, and Kerdock sequences. However, these sequences do not consider some of the practical aspects of modulation, such as maintaining a low peak to average power ratio (PAR). Modulation formats that are intended to reduce PAR can impair or destroy the desired correlation properties of the designed sequences.